Why is the probability of an event always a number between 0 and 1?

The probability of an event is defined as the ratio of favourable outcomes to total outcomes. In the case of discrete distributions these will be represented by numbers, while for continuous distribution they will be measured as areas.

In either case, the first measure is non-negative and the second is positive and so the probability is greater than 0. Also, the number of favourable outcomes cannot be greater than the total so the probability must be at most 1.